Exercise 1 Page 167

Examining the figure, we see that $x^{\circ }$ and $61^{\circ }$ are vertical angles. Therefore, by the Vertical Angles Congruence Theorem, we know that these angles are congruent. To find $y,$ we can either use the fact that $x^{\circ }$ and $y^{\circ }$ are alternate exterior angles or we can use that $61^{\circ }$ and $y^{\circ }$ are corresponding angles. If we use that $61^{\circ }$ and $y^{\circ }$ are corresponding angles, we know by the Corresponding Angles Theorem that they are congruent.